if 5cosa + 3 = 0 and 180<a<360 , find the value of 3tana + 25sin^2a

cosa = -0.6

a = 126.87 degrees or 233.13 degrees

Your requirement that 180<a<360 degrees requires you to pick the second value for a.

Now calculate 3tana + 25sin^2a
I get 4 + 16 = 20.